honesty: screening-indicator framing + ED/4x4 finite-size caveat

README.md

@@ -139,11 +139,22 @@ A_d(δ) table is in `scoring_meta.json`; the pipeline is in `pipeline/`.
 - **Provisional** — your submitted estimate, on the same scale; appears instantly.
 - **Verified** — the organizers' precise solver at the material's filling sets the official rank.
 
-**Honest interpretation:** a higher index means a stronger d-wave pairing *tendency* — a better
-candidate to investigate — **not** a guaranteed critical temperature (Tc) or a confirmed
-superconductor. The effective model is an explicit **single-band approximation** (N(E_F) and δ from
-DFT, t from the active-band width, U/t = 8 as a control). You compete by computing a better,
-material-specific A_d with your own many-body method.
+**Honest interpretation:** the index is a **d-wave pair-correlation screening indicator**, not a
+guaranteed critical temperature (Tc) or a confirmed superconductor. Two caveats we state plainly:
+
+- **Not proven interaction-driven pairing.** A_d comes from a d-wave-biased variational (NQS/AGP)
+  wavefunction, so it measures the pair correlation that a paired trial state sustains — not an
+  unbiased proof that the Hubbard model itself wants d-wave. Independent exact-diagonalization (ED)
+  cross-checks (contributed by participants) and our own control runs (d-wave vs Fermi-sea on a
+  common 4×4 cluster) show the enhancement over the non-interacting case is **not monotonic and is
+  dominated by finite-size effects** — consistent with the modern result that the pure 2D Hubbard
+  model shows no robust d-wave superconductivity at U/t = 8 (Qin et al., *Science* 2020). Treat the
+  A_d(δ) "dome" as partly a finite-size/ansatz feature.
+- **Single-band approximation** (N(E_F) and δ from DFT, t from the active-band width, U/t = 8 as a
+  control).
+
+Use the index to **rank and prioritize candidates**, not to claim superconductivity. You compete by
+computing a better, material-specific pairing estimate with your own many-body method.
 
 ## Tracks & prizes (total US $3,000)